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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is T1 when for all points $x \\neq y$ of $X$ there is an [[open set|01ZQQDCERP]] $U$ with $x \\in U$ and $y \\notin U$.\n\n## Remarks\n\nA space is T1 if and only if each set $\\{x\\}$ with $x \\in X$ is [[closed|0G5AV9Q4RR]].\nEach [[Hausdorff space|0MXB4CKHFW]] is T1, and each T1 space is [[T0|0R3B7DX55J]].\nAn infinite set with the [[cofinite topology|0B906ZBTMZ]] is T1 but not Hausdorff. In fact, the cofinite topology is the coarsest T1 topology on a set.\n\n## Explanations\n\n### L1 human\n\nIn a T1 space, for two distinct points, each point has an open set around it that does not contain the other point.\nThis is the same as saying that single points are closed.\n",
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